The Three-Point Problem in the Field

Every field geologist eventually runs into the same situation: you know the elevation of a bedding contact, a fault plane, or an ore vein at three separate locations, from outcrop, from a topographic map, or from drill hole tops, but you were not able to measure strike and dip directly with a compass. The three-point problem exists to solve exactly that. Any three points that are not in a straight line pin down one unique plane in space, and once you have that plane, its strike and dip fall out of the geometry with no field measurement required.

This calculator solves the problem the same way a structural geology course teaches it on paper, by treating the three points as vectors, finding the plane’s normal vector, and reading strike and dip straight off that normal. It is the same logic behind the classic graphical construction with a topographic map and a protractor, just done exactly rather than by hand.

Checking the Method With a Simple Case

A good way to trust a calculator is to feed it a case simple enough to check by hand. Take three points: A at (0 ft East, 0 ft North, 1000 ft elevation), B at (0 ft East, 1000 ft North, 1000 ft elevation), and C at (500 ft East, 0 ft North, 500 ft elevation). Points A and B sit at the same elevation and both sit on the north-south line, so that line is the strike, striking due north (000 degrees). Point C sits 500 ft east of A and 500 ft lower, a 1:1 slope, which is exactly 45 degrees of dip. Entering these three points into the calculator above returns strike of 000 degrees and dip of 45 degrees to the east, matching the hand check exactly. This is the same graphical logic described in the classic three-point construction method; for a walkthrough of the paper-and-protractor version, see Geological Digressions: Solving the Three-Point Problem.

Reading Quadrant Bearings and the Right-Hand Rule

The calculator reports strike and dip direction both as compass azimuths (0 to 360 degrees) and as quadrant bearings, since field notebooks and published maps use both conventions. Strike follows the right-hand rule: point your right thumb along the reported strike bearing and your curled fingers point in the direction of dip. Because strike describes a line rather than a direction, the bearing shown is equivalent to its reverse, a strike of 045 degrees describes the same line as 225 degrees, and either is correct depending on which end of the outcrop you are standing at.

Common Mistakes

• Entering northing and easting in the wrong fields, which silently rotates the whole solution by 90 degrees.
• Picking three points that are nearly collinear, which makes the plane poorly constrained even though the math still returns an answer.
• Forgetting that strike is a line, not a direction, and reporting it 180 degrees off from the map convention being used.
• Mixing elevation datums between points, for example combining a GPS ellipsoid height with a driller’s KB-referenced depth.

Who Uses This

• Field and exploration geologists solving strike and dip from outcrop elevations or old drill hole tops without a fresh compass reading.
• Structural geology students working through the three-point problem as an alternative to the graphical stereonet method.
• Mining and reservoir geologists checking a structure contour interpretation against three known control points.

Try It Above

Load the example to see the default three points solved, or clear the fields and enter your own easting, northing, and elevation for each point. The strike, dip, and dip direction update live as you type, along with the full plane equation if you want to check the normal vector yourself.

Related Calculators and References

Once you have a dip from this calculator, the True Stratigraphic Thickness Calculator converts a measured interval into true bed thickness using that dip. If you are working with offset beds across a fault rather than a single plane, the Fault Throw, Heave, and Net Slip Calculator picks up from there. For background on the graphical three-point construction this calculator replicates, see Geological Digressions: Solving the Three-Point Problem.